A root-finding algorithm is a numerical method, or algorithm, for finding a value x such that f(x) = 0, for a given functionf. Such an x is called a root of the function f.

This article is concerned with finding real or complex roots, approximated as floating point numbers. Finding integer roots or exact algebraic roots are separate problems, whose algorithms have little in common with those discussed here. (See: Diophantine equation as for integer roots)